Set Based Logic Programming

Abstract

We propose a set of desiderata for extensions of Answer Set Programming to capture domains where the objects of interest are infinite sets and yet we can still process ASP programs effectively. We propose two different schemes to do this. One is to extend cardinality type constraints to set constraints which involve codes for finite, recursive and recursively enumerable sets. A second scheme to modify logic programming to reason about sets directly. In this setting, we can also augment logic programming with certain
monotone inductive operators so that we can reason about families of sets which have structure such a closed sets of a topological space or
subspaces of a vector space. We observe that under such conditions, the classic Gelfond-Lifschitz construction generalizes to at least two different notions of stable models.